Question

draw the image of △abc under the translation (x,y)→(x,y + 3).

Explanation:

Step1: Identify vertex coordinates

Let's assume the coordinates of vertices of $\triangle ABC$ are $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$. From the graph, if we estimate, say $A(- 3,-3)$, $B(1,3)$, $C(-6,2)$.

Step2: Apply the translation rule

The translation rule is $(x,y)\to(x,y + 3)$.
For point $A$: The new - coordinates are $A'(x_1,y_1 + 3)=(-3,-3 + 3)=(-3,0)$.
For point $B$: The new - coordinates are $B'(x_2,y_2 + 3)=(1,3 + 3)=(1,6)$.
For point $C$: The new - coordinates are $C'(x_3,y_3 + 3)=(-6,2+3)=(-6,5)$.

Step3: Plot the new triangle

Plot the points $A'(-3,0)$, $B'(1,6)$ and $C'(-6,5)$ on the same coordinate grid and connect them to form $\triangle A'B'C'$.

Answer:

Plot points $A'(-3,0)$, $B'(1,6)$, $C'(-6,5)$ and connect them to get the image of $\triangle ABC$ under the given translation.